In response to a comment on our Letter [Opt. Lett. 25, 132 (2000)], we reiterate the distinction between the spectral inversion and the spectral phase conjugation processing techniques. The former achieves time reversal of the complex amplitude waveform, whereas the latter performs time reversal of the real electric field.

A real-time spatial-–temporal processor based on cascaded nonlinearities converts space-domain images to time-domain waveforms by the interaction of spectrally decomposed ultrashort pulses and spatially Fourier-transformed images carried by quasi-monochromatic light waves. We use four-wave mixing, achieved by cascaded second-order nonlinearities with type II noncollinear phase matching, for femtosecond-rate processing. We present a detailed analysis of the nonlinear mixing process with waves containing wide temporal and angular bandwidths. The wide bandwidths give rise to phase-mismatch terms in each process of the cascade. We define a complex spatial–temporal filter to characterize the effects of the phase-mismatch terms, modeling the deviations from the ideal system response. New experimental results that support our findings are presented. © 2000 Optical Society of America

Two different realizations of time-reversal experiments of ultrafast waveforms are carried out in real time by use of four-wave mixing arrangements of spectrally decomposed waves. The first, conventional, method is based on phase conjugation of the waveform’s spectrum and achieves time reversal of real amplitude waveforms. The second arrangement of the spectrally decomposed waves spatially inverts the waveform’s spectrum with respect to the optical axis of the processor and achieves true time reversal for complex-amplitude ultrafast waveforms. We compare and contrast these two real-time techniques.  2000 Optical Society of America